Definitely a difficult prospect running all 5 on your own. I do it without a healer, 4 shams and a DK and generally have poor success. I have toyed with the idea of adding a shaman instead of the DK however and just having them spam chain heal. As heyaz says, there is no point adding extra dps to the mix generally, but I have a resto shaman that can spam chain heal until the cows come home and attaching that to my nuke keys should be enough to keep the team up I reckon.

Cheers